import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } enum INF = 10^^9; void main() { try { for (; ; ) { const N = readInt(); const X = readInt(); auto A = new int[N]; foreach (i; 0 .. N) { A[i] = readInt(); } A.sort; long prod = 1; foreach (i; 0 .. N) { prod *= (A[i] + 1); if (prod - 1 > X) { foreach (x; 1 .. X + 1) { write(0); } writeln(); goto failed; } } if (A[0] == 1) { const lb = cast(int)(prod - 1); foreach (x; 1 .. lb) { write(0); } foreach (x; lb .. X + 1) { write(1); } writeln(); goto failed; } { auto ms = new int[1 << N]; auto dp = new int[][1 << N]; foreach (u; 0 .. 1 << N) { ms[u] = 1; foreach (i; 0 .. N) { if (u & 1 << i) { ms[u] = ms[u] / gcd(ms[u], A[i]) * A[i]; } } dp[u] = new int[ms[u]]; dp[u][] = INF; if (!(u & u - 1)) { chmin(dp[u][0], ms[u]); } } foreach (u; 1 .. 1 << N) { foreach (i; 0 .. N) { if (!(u & 1 << i)) { const v = u | 1 << i; foreach (r; 0 .. ms[u]) { if (dp[u][r] < INF) { for (int x = dp[u][r]; ; ) { const z0 = (x + 1) * (A[i] + 1) - 1; for (int z = z0; ; ) { chmin(dp[v][z % ms[v]], z); z += ms[u]; if ((z - z0) % ms[v] == 0) { break; } } for (int z = z0; ; ) { chmin(dp[v][z % ms[v]], z); z += A[i]; if ((z - z0) % ms[v] == 0) { break; } } if (!(u & u - 1)) { break; } x += ms[u]; if ((x - dp[u][r]) % ms[v] == 0) { break; } // break; } } } } } debug { writeln(u, " ", ms[u], " ", dp[u]); } } auto ans = new char[X + 1]; ans[] = '0'; foreach (r; 0 .. ms[$ - 1]) { if (dp[$ - 1][r] < INF) { for (int x = dp[$ - 1][r]; x <= X; ) { ans[x] = '1'; if (N == 1) { break; } x += ms[$ - 1]; } } } writeln(ans[1 .. $]); } failed: } } catch (EOFException e) { } }